Remarks on a conjecture of Chabauty

Hamrouni, Hatem

doi:10.1090/S0002-9939-2010-10717-7

Remarks on a conjecture of Chabauty
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by Hatem Hamrouni PDF

Proc. Amer. Math. Soc. 139 (2011), 1983-1987 Request permission

Abstract:

The Chabauty conjecture for connected nilpotent Lie groups has been proved by S. P. Wang. We show that one reasoning flaw has infiltrated the proof. We therefore give a new proof of the validity of Chabauty’s conjecture in this setup. More generally, we shall prove that the Chabauty conjecture is true for rigid lattices and Zariski dense lattices of connected solvable Lie groups. In particular, the Chabauty conjecture holds for solvable Lie groups of $(R)$-type.

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